Abstract
We study the fourth order nonlinear Schrödinger equation \begin{equation*} i{\partial }_{t}u-\frac{1}{4}\partial _{x}^{4}u=f(u) ,\quad (t,x)\in \mathbb{R}\times \mathbb{R}, \end{equation*} where $f(u) $ is the power nonlinearity of order $p>5.$ The scattering operator is constructed in a neighborhood of the origin in a sutable weighted Sobolev space.
Funding Statement
The work of N.H. is partially supported by JSPS KAKENHI
Grant Numbers JP25220702, JP15H03630. The work of P.I.N. is partially supported by CONACYT
283698 and PAPIIT project IN100616.
Acknowledgment
We are grateful to an unknown referee for many useful suggestions and comments.
Citation
Nakao HAYASHI. Yuichiro KAWAHARA. Pavel I. NAUMKIN. "Scattering operator for the fourth order nonlinear Schrüdinger equation." Hokkaido Math. J. 50 (1) 91 - 109, February 2021. https://doi.org/10.14492/hokmj/2018-907
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